10 14 16 triangle

Acute scalene triangle.

Sides: a = 10   b = 14   c = 16

Area: T = 69.28220323028
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 13.85664064606
Height: hb = 9.89774331861
Height: hc = 8.66602540378

Median: ma = 14.17774468788
Median: mb = 11.35878166916
Median: mc = 9.16551513899

Inradius: r = 3.46441016151
Circumradius: R = 8.08329037687

Vertex coordinates: A[16; 0] B[0; 0] C[5; 8.66602540378]
Centroid: CG[7; 2.88767513459]
Coordinates of the circumscribed circle: U[8; 1.15547005384]
Coordinates of the inscribed circle: I[6; 3.46441016151]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 rad

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 10 ; ; b = 14 ; ; c = 16 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 10+14+16 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-10)(20-14)(20-16) } ; ; T = sqrt{ 4800 } = 69.28 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.28 }{ 10 } = 13.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.28 }{ 14 } = 9.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.28 }{ 16 } = 8.66 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 14**2+16**2-10**2 }{ 2 * 14 * 16 } ) = 38° 12'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+16**2-14**2 }{ 2 * 10 * 16 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 38° 12'48" - 60° = 81° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.28 }{ 20 } = 3.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 38° 12'48" } = 8.08 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 16**2 - 10**2 } }{ 2 } = 14.177 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 10**2 - 14**2 } }{ 2 } = 11.358 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 10**2 - 16**2 } }{ 2 } = 9.165 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.